Your snake might not switch to rats if its been only feed mice; but if you were going to try and switch the sooner you do it the better. I would offer a small rat next time and see how it goes; make sure to pre-scent the room for 30min with the rat. If you're offering frozen thawed you can heat up the rat after defrosting it under a heat lamp in the cage area.

And if you haven't already check out the sticky at the top of the husbandry forum and make sure you have all the right information on temps and humidity.

Good luck!

Edit: Use your judgment when picking the right sized prey item. Make sure it is not thicker than the thickest part of your snake. After looking at the pics I wasn't sure if your snake could handle a small rat.